Computer Program Detail Page

Fermat Light Ray Model

written by
Wolfgang Christian

The Fermat Light Ray model shows a light ray traveling left to right through N homogeneous regions with different refractive indicies. Because light travels in a straight line through a homogenous medium, the path is determined by the vertical coordinates at each boundary. A data table allows users to set the region width w[i] and the refractive index n[i].

Fermat's principal states that the path taken by the light ray between the source and the detector is the path that requires the least time. The speed of light in each region is proportional to the refractive index in that region so the traversal time for region [i] is ?t=n[i]D where D is the ray-segment's length and we have chosen units such that the speed of light in vacuum c=1. The model begins with a straight path (light ray) connecting a source and a detector and computes the travel time for this ray. The travel time is recomputed when the boundary points, the source, or the detector are dragged. The simulation uses a simple Monte Carlo method to find for the minimum-time path when the run button is pressed.

The Fermat Light Ray model was developed using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_csm_ch07_FermatLightRay.jar file will run the program if Java is installed.

Standards (2)

AAAS Benchmark Alignments (2008 Version)

4. The Physical Setting

4E. Energy Transformations

6-8: 4E/M4. Energy appears in different forms and can be transformed within a system. Motion energy is associated with the speed of an object. Thermal energy is associated with the temperature of an object. Gravitational energy is associated with the height of an object above a reference point. Elastic energy is associated with the stretching or compressing of an elastic object. Chemical energy is associated with the composition of a substance. Electrical energy is associated with an electric current in a circuit. Light energy is associated with the frequency of electromagnetic waves.

AAAS Benchmark Alignments (1993 Version)

4. THE PHYSICAL SETTING

E. Energy Transformations

4E (9-12) #2. Heat energy in a material consists of the disordered motions of its atoms or molecules. In any interactions of atoms or molecules, the statistical odds are that they will end up with less order than they began?that is, with the heat energy spread out more evenly. With huge numbers of atoms and molecules, the greater disorder is almost certain.

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